Algebraiska strukturer
Algebraic Structures

FMAN10, 7,5 credits, A (Second Cycle)

General Information

Elective for: C4-ks, C4-sec, D4-ks, F3, Pi2-pvLanguage of instruction: The course will be given in English on demand

Aim

The aim of the course is to give an introduction to the
fundamental concepts and structures of abstract algebra, with
particular regard to subjects of importance in applications in,
e.g., computer science, information theory, physics and chemistry.
The course also aims to give a deeper understanding of the basic
concepts in other areas of mathematics. Furthermore, the course
should develop the students' ability to solve problems and to
understand mathematical text.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

be able to describe basic properties of integers and
polynomials, and be able to compute with congruences modulo these
objects.

be able to describe basic properties of important concepts in
abstract algebra; ring, ideal, quotient ring, group and field.

be able to explain, in writing and orally, the contents of some
central definitions and proofs.

be able to give examples of and illustrate some important
applications of the course contents.

have acquired basic knowledge for further studies in algebra or
subjects based on algebraic methods.

Competences and skills
For a passing grade the student must

be able to independently construct proofs of simple statements
within the framework of the course.

be able to show a good ability to independently, in writing and
orally, explain mathematical reasoning in a well structured way,
with clear logic.

Examination details

Grading scale: THAssessment: Written examination followed, for those who pass, by an oral examination.

Admission

Required prior knowledge: In terms of content, the courses in Calculus and Linear algebra are sufficient. However, the greater mathematical maturity provided by one or more further courses in mathematics is helpful .The number of participants is limited to: NoThe course overlaps following course/s: FMA190

Reading list

Hungerford, T W: Abstract Algebra, An Introduction. Brooks/Cole, 2012, ISBN: 9781111573331. 3rd edition. Since this edition is very expensive the literature may be changed. Otherwise the 2nd edition may be used.